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A140886
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A triangular sequence of coefficients of the characteristic polynomials of Redheffer matrics using Eric Weisstein's matrix function.
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0
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1, 1, -1, 0, -2, 1, -1, -1, 3, -1, -1, 1, 3, -4, 1, -2, 5, -1, -6, 5, -1, -1, 5, -6, -3, 10, -6, 1, -2, 11, -21, 13, 8, -15, 7, -1, -2, 13, -33, 38, -11, -19, 21, -8, 1, -2, 16, -52, 86, -69, 7, 34, -28, 9, -1, -1, 12, -54, 124, -155, 90, 13, -56, 36, -10, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Row sums are: {1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, ...}
Inspired by Mats Granvik's sequence A140865, the sequence is the usual matrix based polynomial sequence type.
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LINKS
| Eric Weisstein's World of Mathematics, Redheffer Matrix
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FORMULA
| t(n,m)=Coefficients( CharacteristicPolynomials(Redheffer(d))).
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EXAMPLE
| {1},
{1, -1},
{0, -2, 1},
{-1, -1,3, -1},
{-1, 1, 3, -4, 1},
{-2, 5, -1, -6, 5, -1},
{-1, 5, -6, -3, 10, -6, 1},
{-2, 11, -21, 13, 8, -15, 7, -1},
{-2, 13, -33, 38, -11, -19, 21, -8, 1},
{-2, 16, -52, 86, -69,7, 34, -28, 9, -1},
{-1, 12, -54, 124, -155, 90, 13, -56, 36, -10, 1}
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MATHEMATICA
| Redheffer[d_] := SparseArray[{{i_, 1} -> 1, {i_, j_} /; Mod[j, i] == 0 -> 1}, {d, d}] a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[Redheffer[d], x], x], {d, 1, 10}]] Flatten[a]
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CROSSREFS
| Cf. A140865.
Sequence in context: A115561 A115622 A108886 * A001492 A054576 A199515
Adjacent sequences: A140883 A140884 A140885 * A140887 A140888 A140889
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KEYWORD
| uned,tabl,sign
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jul 23 2008
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